List questions from continued-fractions

Published on 06 Nov 2019 - 9:03

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Continued fraction expansion of $\sqrt{d^2+1}$

Published on 08 Nov 2019 - 19:29

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Simple continued fraction of $\sqrt{d}$ with period of shortest length $3$

Published on 08 Nov 2019 - 21:20

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Find n-th convergent of continued fraction

Published on 08 Nov 2019 - 23:26

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$1+\frac{3+\frac{5+\frac{⋰}{6}}{4}}{2}$

Published on 14 Nov 2019 - 4:41

39

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State conditions for which $[a_0;a_1,\cdots, a_n] < [b_0; b_1,\cdots, b_{n+1}] $

Published on 14 Nov 2019 - 10:35

232

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$\frac{d}{dx} \frac{1}{x+\frac{1}{x+\frac{1}{ \ddots}}}$, the derivative of an infinite continued fraction.

Published on 29 Nov 2019 - 22:50

134

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The structure of numbers that are not "Khinchin random."

Published on 25 Mar 2026 - 18:08

172

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Is Khinchin's constant really about real numbers?

Published on 02 Dec 2019 - 12:08

49

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To determine a fraction

Published on 25 Mar 2026 - 15:15

102

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$1 + \frac1{2+\frac1{2}} + \dots $ diverges.

Published on 05 Dec 2019 - 4:27

51

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Does $i^n$ always have a continued fraction representation in $\mathbb{Z}$?

Published on 05 Dec 2019 - 19:10

95

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Is there a term for continued fractions of the form $[b; b, b, b \dots ]$?

Published on 06 Dec 2019 - 22:36

1.1k

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Closed form for $\ln(e+\cfrac{1}{\ln(e+ \cfrac1\ddots)})$

Published on 25 Mar 2026 - 12:48

497

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Derivative of a finite continued fraction

Published on 07 Dec 2019 - 13:27

List Question

Evaluate $1+\frac{1}{2+\frac{1}{3+\frac{1}{4+\vdots}}}$

Continued fraction expansion of $\sqrt{d^2+1}$

Simple continued fraction of $\sqrt{d}$ with period of shortest length $3$

Find n-th convergent of continued fraction

$1+\frac{3+\frac{5+\frac{⋰}{6}}{4}}{2}$

State conditions for which $[a_0;a_1,\cdots, a_n] < [b_0; b_1,\cdots, b_{n+1}] $

$\frac{d}{dx} \frac{1}{x+\frac{1}{x+\frac{1}{ \ddots}}}$, the derivative of an infinite continued fraction.

The structure of numbers that are not "Khinchin random."

Is Khinchin's constant really about real numbers?

To determine a fraction

$1 + \frac1{2+\frac1{2}} + \dots $ diverges.

Does $i^n$ always have a continued fraction representation in $\mathbb{Z}$?

Is there a term for continued fractions of the form $[b; b, b, b \dots ]$?

Closed form for $\ln(e+\cfrac{1}{\ln(e+ \cfrac1\ddots)})$

Derivative of a finite continued fraction

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